Canonical Problems in Scattering and Potential Theory: Part 1

Canonical Problems in Scattering and Potential Theory: Part 1

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Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified. The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex more

Product details

  • Hardback | 392 pages
  • 163.6 x 249.9 x 26.2mm | 741.5g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 1584881623
  • 9781584881629

Review quote

"self-contained and well written addressed to mathematicians, physicists, and electrical engineers." - Mathematical Reviews "It does...provide a very comprehensive reference work on a method of solution of a wide variety of potential problems involving bodies with edges, and anyone wishing to solve such a problem would be well advised to consult it either for the solution or for possible methods to approach it." -Derek Collins, SIAM Review, Vol 44, No. 2, 2002show more

Table of contents

PART I: CANONICAL STRUCTURES IN POTENTIAL THEORY Mathematical Aspects of Potential Theory Dual or Triple Series and Integral Equations Electrostatic Potential Theory for Open Spherical Shells and Cavities Open Spheroidal Conducting Shells and Cavities Charged Toroidal Shells and Cavities Potential Theory for Conical Structures with Edges Two-Dimensional Potential Theory Rigorous Solution Methods for more Complicated Structures APPENDICES PART II: ACOUSTIC AND ELECTROMAGNETIC DIFFRACTION BY CANONICAL STRUCTURES Mathematical Aspects of Wave Scattering Acoustic Diffraction from a Circular Hole in a Thin Spherical Shell Acoustic Diffraction from a Spherical Shell with Two Holes or an Equatorial Slot Electromagnetic Diffraction from a Circular Hole in a Perfectly Conducting Spherical Shell Electromagnetic Diffraction from a Spherical Shell with Two Circular Holes or an Equatorial Slot Spherical Cavities with Dielectric Inclusions of Spherical Shape Diffraction from Spheroidal Cavities Applications of the Abel Integral Transform to Diffraction by Other Classes of Canonical Scatterers more